You can find dish or platter hangers at Walmarts or Target or any craft store. I have many antique plates hanging on the wall using the hangers I mentioned.

Check to see on the package how much weight it will hold.

.....Jane

Ditto on what newdawn said. Measure the diameter of the plate and then buy the appropriate size plate hanger. They sell them everywhere and are very inexpensive.

A lot of people are using these new adhesive plate hangers now vs. the old wire & spring ones. Click the link to see them at The Container Store.

Here is a link that might be useful: Adhesive Plate Hangers

I'm skeptical of those adhesive plate hangers. They might be fine for a couple years -maybe- but eventually humidity will erode the adhesive and there goes the plate.
Regular plate hangers aren't that obtrusive!

Regular wire/spring plate hangers can be spray painted to match the plate and make them less obtrusive.

I have heard of people using 2-part epoxy to glue pop can tabs to the back of plates as hangers. Haven't yet tried that myself but I think epoxy is quite strong and would work for all but the heaviest plates.

Decorative metal wall plate racks are another alternative. They hold one to several plates on each hanger depending on style. Keeps plates very secure.

Re the adhesive mounts, I think it would just be a matter of checking them now and then to make sure they're securely attached. Definitely use what you're comfortable with though, especially if the plates are valuable.

This is the model of our new house. They used a combo of a plate rack and runner.

I am trying to remember --- someone had hung plates on a tile backsplash using something like the double stick tape? Anyone know what I am thinking of?